16edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~TallKite~~|~~TallKite~~]] and made on <tt>2016-11-~~14 03~~:16:40 UTC</tt>.<br>

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-04 12:13:32 UTC</tt>.<br>

: The original revision id was <tt>~~599360112~~</tt>.<br>

: The original revision id was <tt>601336582</tt>.<br>

: The revision comment was: <tt></tt><br>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>

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==16 Tone Piano Layout Based on the Anti-diatonic Scale==

[[image:16-EDO-PIano-Diagram.png width="748" height="293"]]

This Layout places Mavila[7] on the ~~white~~ keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.

This Layout places Mavila[7] on the black keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.

=Rank two temperaments=

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===MOS that support metallic harmony===

Mavila 7 contains two hard triads on degrees 1 and 4 and two soft triads on degrees 2 and 6. The other three chords

are wide symmetrical triads 0-1050-1050. Mavila 9 ~~introduced~~ two more soft triads while the Wilson scale introduces two more hard triads.

are wide symmetrical triads 0-1050-1050. Mavila 9 introduces two more soft triads while the Wilson scale introduces two more hard triads.

See [[Metallic Harmony]].

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=Commas=

16 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] < 16 25 37 45 55 59 |.)

16 EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] < 16 25 37 45 55 59/1 |.)

||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||

||= 135/128 ||< | -7 3 1 > ||> 92.18 ||= Major Chroma ||= Major Limma ||= Pelogic Comma ||

||= 648/625 ||< | 3 4 -4 > ||> 62.57 ||= Major Diesis ||= Diminished Comma ||= ||

||= 3125/3072 ||< | -10 -1 5 > ||> 29.61 ||= Small Diesis ||= Magic Comma ||= ||

||= ~~1212717/1210381~~ ||< | 23 6 -14 > ||> 3.34 ||= Vishnuzma ||= Semisuper ||= ||

||= ||< | 23 6 -14 > ||> 3.34 ||= Vishnuzma ||= Semisuper ||= ||

||= 36/35 ||< | 2 2 -1 -1 > ||> 48.77 ||= Septimal Quarter Tone ||= ||= ||

||= 525/512 ||< | -9 1 2 1 > ||> 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||= ||

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<h2 id="toc5"><a name="Hexadecaphonic Notation-16 Tone Piano Layout Based on the Anti-diatonic Scale"></a>16 Tone Piano Layout Based on the Anti-diatonic Scale</h2>

<img src="/file/view/16-EDO-PIano-Diagram.png/599092760/748x293/16-EDO-PIano-Diagram.png" alt="16-EDO-PIano-Diagram.png" title="16-EDO-PIano-Diagram.png" style="height: 293px; width: 748px;" /><br />

This Layout places Mavila[7] on the ~~white~~ keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.<br />

This Layout places Mavila[7] on the black keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.<br />

<br />

<h1 id="toc6"><a name="Rank two temperaments"></a>Rank two temperaments</h1>

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<h3 id="toc8"><a name="Rank two temperaments-Harmonizing Mavila/Armodue in 16 EDO-MOS that support metallic harmony"></a>MOS that support metallic harmony</h3>

Mavila 7 contains two hard triads on degrees 1 and 4 and two soft triads on degrees 2 and 6. The other three chords<br />

are wide symmetrical triads 0-1050-1050. Mavila 9 ~~introduced~~ two more soft triads while the Wilson scale introduces two more hard triads.<br />

are wide symmetrical triads 0-1050-1050. Mavila 9 introduces two more soft triads while the Wilson scale introduces two more hard triads.<br />

<br />

See <a class="wiki_link" href="/Metallic%20Harmony">Metallic Harmony</a>.<br />

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<br />

<h1 id="toc9"><a name="Commas"></a>Commas</h1>

16 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes <a class="wiki_link" href="/val">val</a> &lt; 16 25 37 45 55 59 |.)<br />

16 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes <a class="wiki_link" href="/val">val</a> &lt; 16 25 37 45 55 59/1 |.)<br />

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</tr>

<tr>

</td>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-14 03:16:40 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-04 12:13:32 UTC</tt>.<br>
-: The original revision id was <tt>599360112</tt>.<br>
+: The original revision id was <tt>601336582</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 154: / Line 154: @@
 ==16 Tone Piano Layout Based on the Anti-diatonic Scale==
 [[image:16-EDO-PIano-Diagram.png width="748" height="293"]]
-This Layout places Mavila[7] on the white keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.
+This Layout places Mavila[7] on the black keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.
 =Rank two temperaments=
@@ Line 204: / Line 204: @@
 ===MOS that support metallic harmony===
 Mavila 7 contains two hard triads on degrees 1 and 4 and two soft triads on degrees 2 and 6. The other three chords
-are wide symmetrical triads 0-1050-1050. Mavila 9 introduced two more soft triads while the Wilson scale introduces two more hard triads.
+are wide symmetrical triads 0-1050-1050. Mavila 9 introduces two more soft triads while the Wilson scale introduces two more hard triads.
 See [[Metallic Harmony]].
@@ Line 210: / Line 210: @@
 =Commas=
-EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] &lt; 16 25 37 45 55 59 |.)
+EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[val]] &lt; 16 25 37 45 55 59/1 |.)
 ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
 ||= 135/128 ||&lt; | -7 3 1 &gt; ||&gt; 92.18 ||= Major Chroma ||= Major Limma ||= Pelogic Comma ||
 ||= 648/625 ||&lt; | 3 4 -4 &gt; ||&gt; 62.57 ||= Major Diesis ||= Diminished Comma ||=   ||
 ||= 3125/3072 ||&lt; | -10 -1 5 &gt; ||&gt; 29.61 ||= Small Diesis ||= Magic Comma ||=   ||
-||= 1212717/1210381 ||&lt; | 23 6 -14 &gt; ||&gt; 3.34 ||= Vishnuzma ||= Semisuper ||=   ||
+||=   ||&lt; | 23 6 -14 &gt; ||&gt; 3.34 ||= Vishnuzma ||= Semisuper ||=   ||
 ||= 36/35 ||&lt; | 2 2 -1 -1 &gt; ||&gt; 48.77 ||= Septimal Quarter Tone ||=   ||=   ||
 ||= 525/512 ||&lt; | -9 1 2 1 &gt; ||&gt; 43.41 ||= Avicennma ||= Avicenna's Enharmonic Diesis ||=   ||
@@ Line 987: / Line 987: @@
 &lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Hexadecaphonic Notation-16 Tone Piano Layout Based on the Anti-diatonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;16 Tone Piano Layout Based on the Anti-diatonic Scale&lt;/h2&gt;
   &lt;!-- ws:start:WikiTextLocalImageRule:1044:&amp;lt;img src=&amp;quot;/file/view/16-EDO-PIano-Diagram.png/599092760/748x293/16-EDO-PIano-Diagram.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 293px; width: 748px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/16-EDO-PIano-Diagram.png/599092760/748x293/16-EDO-PIano-Diagram.png" alt="16-EDO-PIano-Diagram.png" title="16-EDO-PIano-Diagram.png" style="height: 293px; width: 748px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1044 --&gt;&lt;br /&gt;
-This Layout places Mavila[7] on the white keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.&lt;br /&gt;
+This Layout places Mavila[7] on the black keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Rank two temperaments&lt;/h1&gt;
@@ Line 1,131: / Line 1,131: @@
 &lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Rank two temperaments-Harmonizing Mavila/Armodue in 16 EDO-MOS that support metallic harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;MOS that support metallic harmony&lt;/h3&gt;
   Mavila 7 contains two hard triads on degrees 1 and 4 and two soft triads on degrees 2 and 6. The other three chords&lt;br /&gt;
-are wide symmetrical triads 0-1050-1050. Mavila 9 introduced two more soft triads while the Wilson scale introduces two more hard triads.&lt;br /&gt;
+are wide symmetrical triads 0-1050-1050. Mavila 9 introduces two more soft triads while the Wilson scale introduces two more hard triads.&lt;br /&gt;
 &lt;br /&gt;
 See &lt;a class="wiki_link" href="/Metallic%20Harmony"&gt;Metallic Harmony&lt;/a&gt;.&lt;br /&gt;
@@ Line 1,137: / Line 1,137: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Commas&lt;/h1&gt;
-EDO &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes &lt;a class="wiki_link" href="/val"&gt;val&lt;/a&gt; &amp;lt; 16 25 37 45 55 59 |.)&lt;br /&gt;
+EDO &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes &lt;a class="wiki_link" href="/val"&gt;val&lt;/a&gt; &amp;lt; 16 25 37 45 55 59/1 |.)&lt;br /&gt;
@@ Line 1,198: / Line 1,198: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: center;"&gt;1212717/1210381&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;| 23 6 -14 &amp;gt;&lt;br /&gt;